Seminar Event Detail

Abstract:
An exchange matrix B dominates an exchange matrix B' if they are the same size and if the signs of corresponding entries weakly agree, with the entry of B always having weakly greater absolute value. When B dominates B', interesting things often happen. For example, the mutation fan for B often refines the mutation fan for B'. (In finite type, these are g-vector fans.) The scattering (diagram) fan for B often refines the scattering fan for B'. And there is often an injective homomorphism from the principal-coefficients cluster algebra for B' to the principal-coefficients cluster algebra for B, preserving g-vectors and (less often) sending cluster variables for B' to cluster variables for B.

I call these "phenomena" because the scope of the description "often" is not settled in any of these contexts. Indeed, there are some counterexamples. In this talk, I will give background on the phenomena and present theorems that provide examples of the phenomena, with the goal of establishing that something real and nontrivial is happening.